How did the parity check DRAM chips work?
They are standard 4116 like their brothers. No special workings here.
Parity check itself was done by the same chip as used for parity generation, a 74LS280 (U94), and signalled as NMI with reason on bit 7 (80h) of port 62h, which is port C of the 8255 in U36.
In particular, is there a reason for the gap in the motherboard (IBM calls this system board) between the parity check DRAM and the "normal" DRAM above it?
Sure, a nice and orderly look.
This makes the board tidier and aligns the U28 socket with the RAM parity chips to the right.
Looks good, doesn't it?
Is there a reason for this gap?
A nice and pleasing look.
Say, why should it be unusual for board designers to have a sense of symmetry?
In my experience, being a hardware engineer often comes with a heightened desire of orderly structures, which is as well supported with design guidelines taught at school and later enforced by layout guidelines of companies - like IBM had.
It's rewarding and pleasing to look at ones creation, more so if made proper.
While this is still true today, it's even more relevant for back then, when a board like for an Apple II or IBM-PC wasn't layouted in five days, but took several weeks, if not month of intense work (*1).
Having said that, there are also several practical reasons. Having chips nicely aligned eases layout, simplifies debugging and likewise patching. This is especially helpful in an environment like with IBM, where average batch sizes were counted in dozends or hundrets. Here other details are more important than shaving of a few penny in board size or development time.
A lesser question is whether there are any products that utilised the ROM expansion socket (labelled U28)?
The only instance I know was a friend who placed a monitor program there, but that wasn't really a product. I guess there were others. The PC very much started as a disk based machine, ROMs didn't play any major role anymore - not even the ROM-BIOS itself.
*1 - If I do layout today, I spend way more time making it look nice - including pleasant staggering of traces, then it takes to get a circuit to work.